Let $A$ denote an algebra finite dimensional, basic, and connected algebra over a algebraically closed field $K$. We denote by $mod A$ the abelian category whose objects are finitely generated right modules over $A$.

Let $T$ a tilting module. Denote the torsion pair induced by $T$ in $mod A$ by $(\mathcal{T}(T),\mathcal{F}(T))$ (http://en.wikipedia.org/wiki/Tilting_theory).

The book "Elements of the Representation Theory of Associative Algebras: Volume 1: Techniques of Representation Theory" (http://books.google.com.br/books/about/Elements_of_the_Representation_Theory_of.html?id=ayNHpi3tYhQC&redir_esc=y) has an exercise that is hard to do:

If $N$ is an object of the $\mathcal{F}(T)$, then $$ pd \; Ext^1_A (T,N) \leq 1 + max(1, pd \; N). $$ Anyone have an idea?

Ps.: $pd$ is the projective dimension.